A 35kg lawnmower starts from rest. Its pushed with a force of 127N at an angle 40 degrees below horizontal. After 12s it reaches speed of 0.37m/s.
Find acceleration and force of friction.
Attempts: Well I figured out Fnormal=343 my multiplying mass by gravity and assuming as it didn't move vertically the Fn=Fg. I also did 127cos40degrees to get 97.288 as the length on one side. I don't know how to get Ffriction without mue or how to get acceleration. I tried vf=d/t to get d=4.44 and was thinking i could sub that into kinematic equation d=vfxt - a/2 x t^2 and got .12 m/s/s. Pretty sure that I'm. Help's Appreciated.
a = (V-Vo)/t = (0.37-0)/12 = 0.0308
(Fx-Fk) = M*a
(127*Cos40-Fk) = 35 * 0.0308
97.3 - Fk = 1.079
-Fk = 1.079 - 97.3 = -96.2
Fk = 96.2 N. = Force of kinetic friction.
To solve this problem, let's break it down step by step:
1. First, let's calculate the force of gravity acting on the lawnmower. Since the lawnmower's mass is given as 35 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the force of gravity using the formula Fg = m * g, where Fg is the force of gravity, m is the mass, and g is the acceleration due to gravity. In this case, Fg = 35 kg * 9.8 m/s^2 = 343 N. This confirms your calculation.
2. Next, let's resolve the applied force into its horizontal and vertical components. The applied force is given as 127 N at an angle of 40 degrees below the horizontal. To determine the horizontal component of the force, we need to find the cosine of the angle. So, the horizontal component of the force (Fx) can be calculated as Fx = F * cos(angle), where F is the magnitude of the force. In this case, Fx = 127 N * cos(40 degrees) = 97.288 N. This confirms your calculation.
3. Now, let's calculate the acceleration of the lawnmower. We can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (Fnet = m * a). Since there are no other forces acting on the lawnmower horizontally, the net force is equal to the horizontal component of the applied force, which is Fnet = 97.288 N. Rearranging the equation to solve for acceleration, we get a = Fnet / m. Plugging in the values, a = 97.288 N / 35 kg = 2.78 m/s^2. So, the acceleration of the lawnmower is 2.78 m/s^2.
4. Lastly, let's find the force of friction. The force of friction can be calculated using the formula Ffriction = μ * Fn, where μ is the coefficient of friction and Fn is the normal force. Unfortunately, we do not have the coefficient of friction (μ) given in the problem. So, we cannot directly calculate the force of friction without this information.
To summarize:
- The acceleration of the lawnmower is 2.78 m/s^2.
- The force of friction cannot be determined without knowing the coefficient of friction (μ).